Threebody unitarity with isobars revisited
Abstract
The particle exchange model of hadron interactions can be used to describe threebody scattering under the isobar assumption. Here, we start from the 3>3 scattering amplitude for spinless particles, which contains an isobarspectator scattering amplitude. Using a BetheSalpeter Ansatz for the latter, we derive a relativistic threedimensional scattering equation that manifestly fulfills threebody unitarity and twobody unitarity for the subamplitudes. Furthermore, this property holds for energies above breakup and also in the presence of resonances in the subamplitudes.
 Authors:

 George Washington Univ., Washington, DC (United States)
 George Washington Univ., Washington, DC (United States); Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)
 Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)
 Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States); Indiana Univ., Bloomington, IN (United States). Center for Exploration of Energy and Matter, Physics Dept.
 Publication Date:
 Research Org.:
 Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)
 Sponsoring Org.:
 USDOE Office of Science (SC), Nuclear Physics (NP) (SC26); National Science Foundation (NSF)
 OSTI Identifier:
 1389749
 Report Number(s):
 JLABTHY172496; DOE/OR/231774206; arXiv:1706.06118
Journal ID: ISSN 14346001; PII: 920
 Grant/Contract Number:
 AC0506OR23177; SC001658; PHY1452055; 1415459
 Resource Type:
 Accepted Manuscript
 Journal Name:
 European Physical Journal. A
 Additional Journal Information:
 Journal Volume: 53; Journal Issue: 9; Journal ID: ISSN 14346001
 Publisher:
 Springer
 Country of Publication:
 United States
 Language:
 English
 Subject:
 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
Citation Formats
Mai, M., Hu, B., Döring, M., Pilloni, A., and Szczepaniak, A. Threebody unitarity with isobars revisited. United States: N. p., 2017.
Web. doi:10.1140/epja/i2017123684.
Mai, M., Hu, B., Döring, M., Pilloni, A., & Szczepaniak, A. Threebody unitarity with isobars revisited. United States. doi:10.1140/epja/i2017123684.
Mai, M., Hu, B., Döring, M., Pilloni, A., and Szczepaniak, A. Fri .
"Threebody unitarity with isobars revisited". United States. doi:10.1140/epja/i2017123684. https://www.osti.gov/servlets/purl/1389749.
@article{osti_1389749,
title = {Threebody unitarity with isobars revisited},
author = {Mai, M. and Hu, B. and Döring, M. and Pilloni, A. and Szczepaniak, A.},
abstractNote = {The particle exchange model of hadron interactions can be used to describe threebody scattering under the isobar assumption. Here, we start from the 3>3 scattering amplitude for spinless particles, which contains an isobarspectator scattering amplitude. Using a BetheSalpeter Ansatz for the latter, we derive a relativistic threedimensional scattering equation that manifestly fulfills threebody unitarity and twobody unitarity for the subamplitudes. Furthermore, this property holds for energies above breakup and also in the presence of resonances in the subamplitudes.},
doi = {10.1140/epja/i2017123684},
journal = {European Physical Journal. A},
number = 9,
volume = 53,
place = {United States},
year = {2017},
month = {9}
}
Free Publicly Available Full Text
Publisher's Version of Record
Other availability
Cited by: 15 works
Citation information provided by
Web of Science
Web of Science
Save to My Library
You must Sign In or Create an Account in order to save documents to your library.
Works referenced in this record:
Hadron Spectroscopy with CLAS and CLAS12
journal, January 2015
 Glazier, D. I.
 Acta Physica Polonica B Proceedings Supplement, Vol. 8, Issue 2
Threebody final state interaction in η→ 3π updated
journal, August 2017
 Guo, P.; Danilkin, I. V.; FernándezRamírez, C.
 Physics Letters B, Vol. 771
Spectrum of ThreeBody Bound States in a Finite Volume
journal, March 2015
 Meißner, UlfG.; Ríos, Guillermo; Rusetsky, Akaki
 Physical Review Letters, Vol. 114, Issue 9
Relativistic ThreeBody Theory with Applications to $\pi N$ Scattering
journal, October 1968
 Aaron, R.; Amado, R. D.; Young, J. E.
 Physical Review, Vol. 174, Issue 5
Coupledchannel analysis of ${D}^{+}\to {K}^{}{\pi}^{+}{\pi}^{+}$ decay
journal, January 2016
 Nakamura, Satoshi X.
 Physical Review D, Vol. 93, Issue 1
A threebody calculation of πd scattering
journal, March 1976
 Thomas, A. W.
 Nuclear Physics A, Vol. 258, Issue 3
Relating the finitevolume spectrum and the twoandthreeparticle $S$ matrix for relativistic systems of identical scalar particles
journal, April 2017
 Briceño, Raúl A.; Hansen, Maxwell T.; Sharpe, Stephen R.
 Physical Review D, Vol. 95, Issue 7
Analysis of ThreeHadron Final States
journal, October 1973
 Aaron, R.; Amado, R. D.
 Physical Review Letters, Vol. 31, Issue 18
Binding energy of the $X(3872)$ at unphysical pion masses
journal, December 2015
 Baru, V.; Epelbaum, E.; Filin, A. A.
 Physical Review D, Vol. 92, Issue 11
Dispersiontheoretical analysis of the D + → K − π + π + Dalitz plot
journal, October 2015
 Niecknig, Franz; Kubis, Bastian
 Journal of High Energy Physics, Vol. 2015, Issue 10
Unitarity effects in pionproduction isobar amplitudes
journal, October 1975
 Aaron, Ronald; Thompson, Richard H.; Amado, Ralph D.
 Physical Review D, Vol. 12, Issue 7
The COMPASS experiment at CERN
journal, July 2007
 Abbon, P.; Albrecht, E.; Alexakhin, V. Yu.
 Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, Vol. 577, Issue 3
E (1420) meson as a KK¯ π molecule
journal, August 1990
 Longacre, R. S.
 Physical Review D, Vol. 42, Issue 3
Analytic properties of the scattering amplitude and resonances parameters in a meson exchange model
journal, October 2009
 Döring, M.; Hanhart, C.; Huang, F.
 Nuclear Physics A, Vol. 829, Issue 34
Relativistic, modelindependent, threeparticle quantization condition
journal, December 2014
 Hansen, Maxwell T.; Sharpe, Stephen R.
 Physical Review D, Vol. 90, Issue 11
Three particles in a finite volume
journal, May 2012
 Polejaeva, K.; Rusetsky, A.
 The European Physical Journal A, Vol. 48, Issue 5
Nucleon resonances within a dynamical coupledchannels model of $\pi N$ and $\gamma N$ reactions
journal, September 2013
 Kamano, H.; Nakamura, S. X.; Lee, T. S. H.
 Physical Review C, Vol. 88, Issue 3
$\omega \to {\pi}^{0}{\gamma}^{*}$ and $\varphi \to {\pi}^{0}{\gamma}^{*}$ transition form factors in dispersion theory
journal, September 2012
 Schneider, Sebastian P.; Kubis, Bastian; Niecknig, Franz
 Physical Review D, Vol. 86, Issue 5
Heavyquark QCD exotica
journal, March 2017
 Lebed, Richard F.; Mitchell, Ryan E.; Swanson, Eric S.
 Progress in Particle and Nuclear Physics, Vol. 93
Recoil corrections in antikaondeuteron scattering
journal, March 2015
 Mai, Maxim; Baru, Vadim; Epelbaum, Evgeny
 Physical Review D, Vol. 91, Issue 5
Unitary coupledchannels model for threemesons decays of heavy mesons
journal, December 2011
 Kamano, H.; Nakamura, S. X.; Lee, T. S. H.
 Physical Review D, Vol. 84, Issue 11
Expressing the threeparticle finitevolume spectrum in terms of the threetothree scattering amplitude
journal, December 2015
 Hansen, Maxwell T.; Sharpe, Stephen R.
 Physical Review D, Vol. 92, Issue 11
Minimal threebody equations with finiterange effects
journal, October 1975
 Amado, R. D.
 Physical Review C, Vol. 12, Issue 4
Towards threebody unitarity in ${D}^{+}\to {K}^{}{\pi}^{+}{\pi}^{+}$
journal, November 2011
 Magalhães, P. C.; Robilotta, M. R.; Guimarães, K. S. F. F.
 Physical Review D, Vol. 84, Issue 9
Minimal ThreeBody Scattering Theory
journal, July 1974
 Amado, R. D.
 Physical Review Letters, Vol. 33, Issue 5
Coupledchannel dynamics in the reactions πN → πN, ηN, KΛ, KΣ
journal, April 2013
 Rönchen, D.; Döring, M.; Huang, F.
 The European Physical Journal A, Vol. 49, Issue 4
The optical potential on the lattice
journal, June 2016
 Agadjanov, Dimitri; Döring, Michael; Mai, Maxim
 Journal of High Energy Physics, Vol. 2016, Issue 6
Dispersive analysis of ω→3π and ϕ→3π decays
journal, May 2012
 Niecknig, Franz; Kubis, Bastian; Schneider, Sebastian P.
 The European Physical Journal C, Vol. 72, Issue 5
Threebody resonances in twomeson–onebaryon systems
journal, April 2008
 Martínez Torres, A.; Khemchandani, K. P.; Oset, E.
 Physical Review C, Vol. 77, Issue 4
Nature of the ${a}_{1}(1420)$
journal, May 2015
 Mikhasenko, M.; Ketzer, B.; Sarantsev, A.
 Physical Review D, Vol. 91, Issue 9
Threebody $D\overline{D}\pi $ dynamics for the $X(3872)$
journal, October 2011
 Baru, V.; Filin, A. A.; Hanhart, C.
 Physical Review D, Vol. 84, Issue 7
Relevance of complex branch points for partial wave analysis
journal, July 2011
 Ceci, S.; Döring, M.; Hanhart, C.
 Physical Review C, Vol. 84, Issue 1
Unitary analytic isobar model for the reaction nucleonmeson to nucleonmesonmeson
journal, June 1978
 Aitchison, I. J. R.; Brehm, J. J.
 Physical Review D, Vol. 17, Issue 11
Theoretical support for the $\pi (1300)$ and the recently claimed ${f}_{0}(1790)$ as molecular resonances
journal, October 2011
 Martínez Torres, A.; Khemchandani, K. P.; Jido, D.
 Physical Review D, Vol. 84, Issue 7
Dispersion relations for $$\eta '\rightarrow \eta \pi \pi $$ η ′ → η π π
journal, July 2017
 Isken, Tobias; Kubis, Bastian; Schneider, Sebastian P.
 The European Physical Journal C, Vol. 77, Issue 7
PionPion Scattering and ${K}^{\pm}\to 3\pi $ Decay
journal, August 1960
 Khuri, N. N.; Treiman, S. B.
 Physical Review, Vol. 119, Issue 3
Scattering of unstable particles in a finite volume: The case of $\pi \rho $ scattering and the ${a}_{1}(1260)$ resonance
journal, March 2012
 Roca, L.; Oset, E.
 Physical Review D, Vol. 85, Issue 5
Three  Meson Resonances in a Relativistic Faddeev  Type Approach
journal, September 1972
 Mennessier, G.; Pasquier, J. Y.; Pasquier, R.
 Physical Review D, Vol. 6, Issue 5
Dynamical coupledchannels model of ${K}^{}p$ reactions: Determination of partialwave amplitudes
journal, December 2014
 Kamano, H.; Nakamura, S. X.; Lee, T. S. H.
 Physical Review C, Vol. 90, Issue 6
Eta photoproduction in a combined analysis of pion and photoninduced reactions
journal, June 2015
 Rönchen, D.; Döring, M.; Haberzettl, H.
 The European Physical Journal A, Vol. 51, Issue 6
Faddeevchiral unitary approach to the ${K}^{}d$ scattering length
journal, March 2013
 Mizutani, T.; Fayard, C.; Saghai, B.
 Physical Review C, Vol. 87, Issue 3
Dispersive approaches for threeparticle final state interaction
journal, October 2015
 Guo, Peng; Danilkin, I. V.; Szczepaniak, Adam P.
 The European Physical Journal A, Vol. 51, Issue 10
Isobar formalism and onepionexchange partialwave cross sections in $\pi N\to \pi \pi N$
journal, July 1977
 Aaron, Ronald; Amado, R. D.; Arndt, Richard A.
 Physical Review D, Vol. 16, Issue 1
Dispersive analysis of $\omega /\varphi \to 3\pi ,\pi {\gamma}^{*}$
journal, May 2015
 Danilkin, I. V.; FernándezRamírez, C.; Guo, P.
 Physical Review D, Vol. 91, Issue 9
Remarks on study of $X(3872)$ from effective field theory with pionexchange interaction
journal, February 2015
 Baru, V.; Epelbaum, E.; Filin, A. A.
 Physical Review D, Vol. 91, Issue 3
New approach to the theory of coupled πNNNN systems
journal, April 1980
 Avishai, Y.; Mizutani, T.
 Nuclear Physics A, Vol. 338, Issue 2
Relativistic isobar model: Spinless particles
journal, May 1976
 Aaron, R.; Amado, R. D.
 Physical Review D, Vol. 13, Issue 9
Hadron Spectroscopy at BESIII
journal, April 2016
 Fang, Shuangshi
 Nuclear and Particle Physics Proceedings, Vol. 273275
Reduction of the threeparticle collision problem to multichannel twoparticle LippmannSchwinger equations
journal, June 1967
 Alt, E. O.; Grassberger, P.; Sandhas, W.
 Nuclear Physics B, Vol. 2, Issue 2
The Physics of the B Factories
journal, November 2014
 Bevan, A. J.; Golob, B.; Mannel, Th.
 The European Physical Journal C, Vol. 74, Issue 11
Multiquark resonances
journal, January 2017
 Esposito, A.; Pilloni, A.; Polosa, A. D.
 Physics Reports, Vol. 668
Threebody final state interaction in $\eta \to 3\pi $
journal, September 2015
 Guo, Peng; Danilkin, Igor V.; Schott, Diane
 Physical Review D, Vol. 92, Issue 5
Linear Integral Equations for Relativistic Multichannel Scattering
journal, February 1966
 Blankenbecler, R.; Sugar, R.
 Physical Review, Vol. 142, Issue 4
Unified theory of γN→πN , ππN , and πN→πN , ππN reactions
journal, October 1988
 Afnan, I. R.
 Physical Review C, Vol. 38, Issue 4
Threeparticle quantization condition in a finite volume: 2. General formalism and the analysis of data
journal, October 2017
 Hammer, HansWerner; Pang, JinYi; Rusetsky, Akaki
 Journal of High Energy Physics, Vol. 2017, Issue 10, 31 p.
Works referencing / citing this record:
The impact of $K^{+}\Lambda$ K + Λ photoproduction on the resonance spectrum
journal, June 2018
 Rönchen, D.; Döring, M.; Meißner, U. G.
 The European Physical Journal A, Vol. 54, Issue 6
The impact of $K^{+}\Lambda$ K + Λ photoproduction on the resonance spectrum
journal, June 2018
 Rönchen, D.; Döring, M.; Meißner, U. G.
 The European Physical Journal A, Vol. 54, Issue 6